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SOLUTIONS OF A GOŁA̧B–SCHINZEL-TYPE FUNCTIONAL EQUATION BOUNDED ON ‘BIG’ SETS IN AN ABSTRACT SENSE
Published online by Cambridge University Press: 05 March 2010
Abstract
It is well known that an exponential real function, which is Lebesgue measurable (Baire measurable, respectively) or bounded on a set of positive Lebesgue measure (of the second category with the Baire property, respectively), is continuous. Here we consider bounded on ‘big’ set solutions of an equation generalizing the exponential equation as well as the Goła̧b–Schinzel equation. Moreover, we unify results into a more general and abstract case.
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- Copyright © Australian Mathematical Publishing Association Inc. 2010
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